Related papers: Parallel Algorithms for the One Sided Crossing Min…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
A matching cut of a graph is a partition of its vertex set in two such that no vertex has more than one neighbor across the cut. The Matching Cut problem asks if a graph has a matching cut. This problem, and its generalization d-cut, has…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
Maximal Clique Enumeration (MCE) is a fundamental graph mining problem, and is useful as a primitive in identifying dense structures in a graph. Due to the high computational cost of MCE, parallel methods are imperative for dealing with…
As massive graphs become more prevalent, there is a rapidly growing need for scalable algorithms that solve classical graph problems, such as maximum matching and minimum vertex cover, on large datasets. For massive inputs, several…
One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…
Orthogonal signal-division multiplexing (OSDM) is an attractive alternative to conventional orthogonal frequency-division multiplexing (OFDM) due to its enhanced ability in peak-to-average power ratio (PAPR) reduction. Combining OSDM with…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…
We develop and extensively evaluate highly scalable distributed-memory algorithms for computing minimum spanning trees (MSTs). At the heart of our solutions is a scalable variant of Boruvka's algorithm. For partitioned graphs with many…
In a series of papers, Avraham, Filtser, Kaplan, Katz, and Sharir (SoCG'14), Kaplan, Katz, Saban, and Sharir (ESA'23), and Katz, Saban, and Sharir (ESA'24) studied a class of geometric optimization problems -- including reverse shortest…
We present a parallel version of the cut-pursuit algorithm for minimizing functionals involving the graph total variation. We show that the decomposition of the iterate into constant connected components, which is at the center of this…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
We study graph connectivity problem in MPC model. On an undirected graph with $n$ nodes and $m$ edges, $O(\log n)$ round connectivity algorithms have been known for over 35 years. However, no algorithms with better complexity bounds were…
We present efficient parallel algorithms for computing maximal matchings in hypergraphs. Our algorithm finds locally maximal edges in the hypergraph and adds them in parallel to the matching. In the CRCW PRAM models our algorithms achieve…
We study the Minimum Crossing Number problem: given an $n$-vertex graph $G$, the goal is to find a drawing of $G$ in the plane with minimum number of edge crossings. This is one of the central problems in topological graph theory, that has…
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…
The increasing use of heterogeneous embedded systems with multi-core CPUs and Graphics Processing Units (GPUs) presents important challenges in effectively exploiting pipeline, task and data-level parallelism to meet throughput requirements…
The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new…
Scenario-based stochastic optimal control problems suffer from the curse of dimensionality as they can easily grow to six and seven figure sizes. First-order methods are suitable as they can deal with such large-scale problems, but may fail…